In digital communications, a signal comprising a number of complex symbols is transmitted through a medium, or channel, to a receiver. Due to channel effects, noise, or non-linear components in a transmitter or receiver, the receiver typically observes a distorted version of the transmitted signal. Thus, the goal of the receiver is to recover the sequence of symbols transmitted by the transmitter from the received signal.
In an attempt to recover the original transmitted sequence of symbols, the receiver applies an equalizer to the received signal, which may comprise a digital representation of an analog waveform representing the signal received at the receiver. The equalizer may recover “hard” information (e.g., a direct estimate of the symbol sequence) or “soft” information (e.g., in the form of a probability distribution) corresponding to the transmitted signal. A well known equalization technique may be implemented in the form of a forward-backward equalizer, which determines a posteriori distributions of the transmitted symbols based on the received signal. Each symbol of the originally transmitted sequence may be determined by obtaining a mode of the a posteriori distributions for the corresponding symbol.